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An Improved PID Controller for the Compliant Constant-Force Actuator Based on BP Neural Network and Smith Predictor

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An Improved PID Controller for the Compliant Constant-Force Actuator Based on BP Neural Network and Smith Predictor applied sciences Article An Improved PID Controller for the Compliant Constant-Force Actuator Based on BP Neural Network and Smith Predictor Guojin Pei 1,2,3, Ming Yu 1,2, Yaohui Xu 1,2, Cui Ma 1,2, Houhu Lai 1,2, Fokui Chen 1,2 and Hui Lin 1,2,* 1 Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China; [email protected] (G.P.); [email protected] (M.Y.); [email protected] (Y.X.); [email protected] (C.M.); [email protected] (H.L.); [email protected] (F.C.) 2 Shenzhen Key Laboratory of Precision Engineering, Shenzhen 518055, China 3 College of Mechanical and Transportation Engineering, China University of Petroleum, Changping, Beijing 102200, China * Correspondence: [email protected] Abstract: A compliant constant-force actuator based on the cylinder is an important tool for the contact operation of robots. Due to the nonlinearity and time delay of the pneumatic system, the traditional proportional–integral–derivative (PID) method for constant force control does not work so well. In this paper, an improved PID control method combining a backpropagation (BP) neural network and the Smith predictor is proposed. Through MATLAB simulation and experimental validation, the results show that the proposed method can shorten the maximum overshoot and the adjustment time compared with traditional the PID method. Keywords: compliant force control; PID; neural network; Smith predictor Citation: Pei, G.; Yu, M.; Xu, Y.; Ma, C.; Lai, H.; Chen, F.; Lin, H. An Improved PID Controller for the 1. Introduction Compliant Constant-Force Actuator Based on BP Neural Network and With the continuous development of industrial automation, the application of robots Smith Predictor. Appl. Sci. 2021, 11, is becoming more extensive [1]. Robots are required to have the capabilities of precise 2685. https://doi.org/10.3390/ force perception and force control in contact operations such as grinding, polishing and app11062685 assembly, as subtle changes in the contact force will affect processing quality [2,3]. In recent years, a number of compliant constant-force actuators have been developed based Academic Editor: Manuel Armada on gasbag [4], voice coil motor [5], cylinder [6–9], artificial muscle [10,11] and special mechanical structures [12,13]. Among them, the pneumatic system based on the cylinder is Received: 16 December 2020 the most widely used because air has good compliance. However, the pneumatic system Accepted: 12 March 2021 is a complex nonlinear system, due to the compressibility of air and the inevitable static Published: 17 March 2021 friction [14]. Therefore, achieving precise force control in the pneumatic system is both practical and challenging. Publisher’s Note: MDPI stays neutral In recent years, intelligent control algorithms such as fuzzy logic, neural networks with regard to jurisdictional claims in and expert systems have been developed rapidly, providing new ideas for the design of a published maps and institutional affil- pneumatic force control system [15–21]. The traditional proportional–integral–derivative iations. (PID) method is a classic controller that was used for years because of its simplicity and effectiveness. However, with the requirement of low force control error in modern industry, it is difficult for a traditional PID controller to achieve the expected control quality indices in such complex nonlinear systems. Scholars made great efforts in the Copyright: © 2021 by the authors. combination of intelligent control and traditional PID control, especially the combination Licensee MDPI, Basel, Switzerland. of a backpropagation neural network (BPNN) and a PID controller. Kang et al. applied the This article is an open access article BPNN-PID control method to the pneumatic force control system and demonstrated that distributed under the terms and the controller had better robustness and control performance [17–19]. conditions of the Creative Commons These intelligent controllers have improved the performance of force control in the Attribution (CC BY) license (https:// pneumatic nonlinear system to some extent. Nevertheless, besides the nonlinear property, creativecommons.org/licenses/by/ there is a pure time delay link in the pneumatic systems based on pneumatic cylinders [22]. 4.0/). Appl. Sci. 2021, 11, 2685. https://doi.org/10.3390/app11062685 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 2685 2 of 19 Appl. Sci. 2021, 11, 2685 2 of 18 there is a pure time delay link in the pneumatic systems based on pneumatic cylinders In[22]. the In implementation the implementation of such of such stabilizing stabilizin feedbackg feedback control, control, even even a smalla small time time delay delay may causemay cause destabilization destabilization of the of controllerthe controller [23], [23], because because the the time time delay delay makes makes the the controlled con- variablestrolled variables unable unable to reflect to reflect the disturbance the disturbance of the of systemthe system in time, in time, which which will will produce pro- a largerduce a overshoot larger overshoot and longer and longer adjustment adjustment time [time24]. [24]. InIn some other other control control systems, systems, such such as as chem chemicalical engineering, engineering, oil oilrefining, refining, metallurgy metallurgy andand heatheat engineeringengineering processprocess controlcontrol systems,systems, thethe SmithSmithpredictor predictorhas has been been used used effectively effec- fortively compensating for compensating for the for pure the pure time time delay de [lay25, 26[25,26].]. For For a given a give signal,n signal, the the Smith Smith predictor pre- estimatesdictor estimates the dynamic the dynamic characteristics characteristics of the systemof the system under under disturbance disturbance in advance in advance and then compensatesand then compensates the time delaythe time error delay to reduceerror to the reduce overshoot the overshoot of the system of the and system shorten and the shorten the adjustment process [27]. However, the Smith predictor depends on the system adjustment process [27]. However, the Smith predictor depends on the system model, so model, so its performance is very sensitive to modeling errors. Pneumatic force control its performance is very sensitive to modeling errors. Pneumatic force control systems are systems are usually complex and time-varying, so it is difficult to build accurate mathe- usually complex and time-varying, so it is difficult to build accurate mathematical models. matical models. As a result, the Smith predictor is rarely used in such systems to the best As a result, the Smith predictor is rarely used in such systems to the best of our knowledge. of our knowledge. In order to improve the modeling accuracy and make the Smith predictor suitable for In order to improve the modeling accuracy and make the Smith predictor suitable for use in a pneumatic force control system, this paper brings the neural network algorithm into use in a pneumatic force control system, this paper brings the neural network algorithm theinto structure the structure of the of Smiththe Smith predictor. predictor. Moreover, Moreover, the the improved improved Smith Smith predictor predictor is connectedis con- withnected the with BPNN-PID the BPNN-PID controller controller to optimize to opti themize overall the overall control control performance. performance. Therefore, There- the structurefore, the structure of this improved of this improved controller contro (backpropagationller (backpropagation neural network-Smithneural network-Smith predictor- proportional–integral–derivativepredictor-proportional–integral–derivative (BPNN-SP-PID)) (BPNN-SP-PID)) proposed inproposed this paper in isthis mainly paper divided is intomainly two divided parts. Oneinto two part parts. is to One combine part is the to artificialcombine the neural artificial network neural (ANN) network with (ANN) the PID controller.with the PID An controller. online learning An online backpropagation learning backpropagation neural network neural ANN1 network is taken ANN1 to adjustis thetaken PID to adjust parameters the PID adaptively parameters to adaptively improve to the improve dynamic the performancedynamic performance of the controller. of the Thecontroller. other partThe other is to combinepart is to combine the artificial the artificial neural networkneural network with the with Smith the Smith predictor. pre- A neuraldictor. networkA neural ANN2network is usedANN2 for is identifyingused for identifying the nonlinear the nonlinear model of model the controlled of the con- object totrolled improve object its to modelingimprove its accuracy, modeling so accuracy, that the so Smith that the predictor Smith predictor can compensate can compen- for the puresate for time the delay pure time well. delay The integrationwell. The integration of a BPNN-PID of a BPNN-PID controller controller and the and Smith the Smith predictor improvespredictor improves the robustness the robustness and speed and of speed the pneumatic of the pneumatic force control force control system. system. TheThe restrest ofof thisthis paperpaper isis organizedorganized as follows. Section 22 introducesintroduces the system structurestruc- andture modeland model of the of compliant the compliant constant-force constant-forc actuator.e actuator. Section Section3 introduces 3 introduces the the design design of the BPNN-SP-PIDof the BPNN-SP-PID controller. controller. Section Section4 shows 4 shows the simulationthe
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